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Stability of the tetragonal phase of BaZrO3 under high pressure

Constance Toulouse, Danila Amoroso, Robert Oliva, Cong Xin, Pierre Bouvier, Pierre Fertey, Philippe Veber, Mario Maglione, Philippe Ghosez, Jens Kreisel, and Mael Guennou
Phys. Rev. B 106, 064105 – Published 16 August 2022
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  • INTRODUCTION
  • METHODS AND EXPERIMENTAL DETAILS
  • RESULTS AND DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    In this paper, we revisit the high pressure behavior of BaZrO3 by a combination of first-principle calculations, Raman spectroscopy and x-ray diffraction under high pressure. We confirm experimentally the cubic-to-tetragonal transition at 10GPa and find no evidence for any other phase transition up to 45GPa, the highest pressures investigated, at variance with past reports. We reinvestigate phase stability with density functional theory considering not only the known tetragonal (I4/mcm) phase but also other potential antiferrodistortive candidates. This shows that the tetragonal phase becomes progressively more stable upon increasing pressure as compared to phases with more complex tilt systems. The possibility for a second transition to another tilted phase at higher pressures, and in particular to the very common orthorhombic Pnma structure, is therefore ruled out.

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    • Received 13 May 2022
    • Revised 14 July 2022
    • Accepted 15 July 2022

    DOI:https://doi.org/10.1103/PhysRevB.106.064105

    ©2022 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Crystal structureHigh-pressure studiesLattice dynamicsPhase transitionsPhononsStructural properties
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Constance Toulouse1,*,†, Danila Amoroso2,*,‡, Robert Oliva1,*,§, Cong Xin3,4, Pierre Bouvier5, Pierre Fertey6, Philippe Veber3,7, Mario Maglione3, Philippe Ghosez8, Jens Kreisel1, and Mael Guennou1

    • 1University of Luxembourg, Department of Physics and Materials Science, 41 rue du Brill, 4422 Belvaux, Luxembourg
    • 2Physics of Nanostructures and Materials (NanoMat), Q-MAT, CESAM, University of Liège, B-4000 Liège, Belgium
    • 3Institut de Chimie de la Matière Condensée de Bordeaux (ICMCB)-UMR 5026, CNRS, Université de Bordeaux, 87 Avenue du Docteur Schweitzer, F-33608 Pessac, France
    • 4Materials Research and Technology Department, Luxembourg Institute of Science and Technology (LIST), 41 rue du Brill, 4422 Belvaux, Luxembourg
    • 5Université Grenoble Alpes, Institut Néel CNRS, 25 Rue des Martyrs, 38042, Grenoble, France
    • 6Synchrotron SOLEIL, L'Orme des merisiers, Saint-Aubin, Gif-sur-Yvette, France
    • 7Institut Lumière Matière (ILM)-UMR 5306, Université Claude Bernard Lyon 1, Campus LyonTech-La Doua, 10 rue Ada Byron, F-69622 Villeurbanne, France
    • 8Theoretical Materials Physics, Quantum Materials Center (Q-MAT), Complex and Entangled Systems from Atoms to Materials (CESAM), University of Liège, B-4000 Liège, Belgium

    • *These authors contributed equally to this work.
    • †constance.toulouse@uni.lu
    • ‡danila.amoroso@uliege.be
    • §robert.olivavidal@uni.lu

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    Vol. 106, Iss. 6 — 1 August 2022

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    Images

    • Figure 1
      Figure 1

      Raman spectra of BaZrO3 single crystals under pressure (a) from 0 to 19GPa when increasing pressure, and (c) between 21 and 12GPa when releasing pressure. The spectra in (a) are classical Stokes spectra, while the spectra in (c) are collected without cutting off the Rayleigh scattering of the laser line, allowing for observation of lower energies. An example of the Lorentzian fits performed on the Raman modes is shown in blue. (b) Pressure dependence of the wavenumbers of the phonon modes derived from the spectra obtained from 0 to 19GPa, the solid symbols show the modes appearing above the transition at 10GPa. (d) Behavior of the two soft modes (and first hard mode) appearing above 10GPa, these frequencies are derived from the spectra shown in (c), fitted with Lorentzian functions.

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    • Figure 2
      Figure 2

      (a) Diffraction patterns of sample S2. Inset: Zoom of the low-angle region. Low-angle fitted peak positions at 45.1GPa are included as red and blue ticks corresponding to I4/mcm and Imma structures, respectively. Note that no diffraction peak is visible where the reflection (011) of an Imma phase would be expected. (b) Top: Rietveld fit (grey line) to a diffraction pattern (black line) acquired at 1.34GPa. Bottom: Rietveld fit assuming tetragonal and orthorhombic phases (red and blue dashed lines, respectively) to a pattern acquired at a pressure of 45.1GPa. Fitted positions for all reflections are included at the bottom as colored ticks. Both panels use the same intensity scale and residuals of the Imma fit are vertically shifted for a better comparison. (c) Pressure dependence of the volume per formula unit ABO3 for the cubic and tetragonal phases (black and red, respectively). Lines are fits to a BM EoS (for the cubic phase a high-pressure extrapolation is included as a black-dashed line). Inset: Bulk modulus as a function of pressure. (d) Top: Tetragonality (c/a ratio) as a function of pressure as obtained from the fitted x-ray diffraction (XRD) patterns of sample S2 (crosses) and adapted DFT calculations (squares). Bottom: Volume (ea) and tetragonal (et) spontaneous strains as obtained from the experiments (crosses), our calculations (open symbols) and calculations published by Granhed et al. [25]. Our reported DFT-values include a pressure shift (+10GPa) as discussed in the text; this is not the case for values taken from Ref. [25] calculated through the hybrid Heyd-Scuseria-Ernzerhof (HSE) functional, which provides a slight larger volume than the one obtained from the WC-functional employed here (cf. Table I in Ref. [25]).

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    • Figure 3
      Figure 3

      [(a),(b),(c)] DFPT phonon dispersion curves in the cubic phase for 20, 40, and 60GPa applied hydrostatic pressure (corresponding lattice parameters a are 4.049 Å, 3.955 Å, and 3.883 Å, respectively). Red, green, and blue phononic branches involve mostly Ba, Zr, and O vibrations, respectively. (d) Computed enthalpies (H), with respect to the cubic phase taken as reference at each pressure. (e) Evolution of the oxygen octahedra rotation angle Θ (in degree, ∘) with hydrostatic external pressure for different rotation patterns.

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